Entropy of the (1+1)-dimensional directed percolation*

We investigate the informational aspect of a (1+1)-dimensional directed percolation which can be regarded as a reaction-diffusion process in a one-dimensional system and is a canonical model of a non-equilibrium continuous phase transition into an absorbing state. Using a tensor network scheme based on a mapping between a state probability distribution and a wave function, we can numerically calculate a time evolution of a state probability distribution. Although the density of active sites has no singular behavior, there is a new singular point in the conventional active phase at which the dynamical behavior of the entanglement entropy changes. The Rényi entropy has a cusp at the same point. The Rényi entropy also shows a universal relaxation at the critical point of the conventional absorbing phase transition.